Optimal. Leaf size=73 \[ -\frac {10125 x^6}{16}-\frac {80595 x^5}{16}-\frac {629505 x^4}{32}-\frac {1661133 x^3}{32}-\frac {28504029 x^2}{256}-\frac {64029233 x}{256}-\frac {39220335}{256 (1-2 x)}+\frac {22370117}{1024 (1-2 x)^2}-\frac {60160485}{256} \log (1-2 x) \]
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Rubi [A] time = 0.04, antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ -\frac {10125 x^6}{16}-\frac {80595 x^5}{16}-\frac {629505 x^4}{32}-\frac {1661133 x^3}{32}-\frac {28504029 x^2}{256}-\frac {64029233 x}{256}-\frac {39220335}{256 (1-2 x)}+\frac {22370117}{1024 (1-2 x)^2}-\frac {60160485}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {64029233}{256}-\frac {28504029 x}{128}-\frac {4983399 x^2}{32}-\frac {629505 x^3}{8}-\frac {402975 x^4}{16}-\frac {30375 x^5}{8}-\frac {22370117}{256 (-1+2 x)^3}-\frac {39220335}{128 (-1+2 x)^2}-\frac {60160485}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {22370117}{1024 (1-2 x)^2}-\frac {39220335}{256 (1-2 x)}-\frac {64029233 x}{256}-\frac {28504029 x^2}{256}-\frac {1661133 x^3}{32}-\frac {629505 x^4}{32}-\frac {80595 x^5}{16}-\frac {10125 x^6}{16}-\frac {60160485}{256} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 66, normalized size = 0.90 \[ -\frac {2592000 x^8+18040320 x^7+60592320 x^6+137206464 x^5+263583600 x^4+621559520 x^3-1569001020 x^2+600903660 x+240641940 (1-2 x)^2 \log (1-2 x)-30126129}{1024 (1-2 x)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 72, normalized size = 0.99 \[ -\frac {2592000 \, x^{8} + 18040320 \, x^{7} + 60592320 \, x^{6} + 137206464 \, x^{5} + 263583600 \, x^{4} + 621559520 \, x^{3} - 910451612 \, x^{2} + 240641940 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 57645748 \, x + 134511223}{1024 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 52, normalized size = 0.71 \[ -\frac {10125}{16} \, x^{6} - \frac {80595}{16} \, x^{5} - \frac {629505}{32} \, x^{4} - \frac {1661133}{32} \, x^{3} - \frac {28504029}{256} \, x^{2} - \frac {64029233}{256} \, x + \frac {290521 \, {\left (1080 \, x - 463\right )}}{1024 \, {\left (2 \, x - 1\right )}^{2}} - \frac {60160485}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 56, normalized size = 0.77 \[ -\frac {10125 x^{6}}{16}-\frac {80595 x^{5}}{16}-\frac {629505 x^{4}}{32}-\frac {1661133 x^{3}}{32}-\frac {28504029 x^{2}}{256}-\frac {64029233 x}{256}-\frac {60160485 \ln \left (2 x -1\right )}{256}+\frac {22370117}{1024 \left (2 x -1\right )^{2}}+\frac {39220335}{256 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 56, normalized size = 0.77 \[ -\frac {10125}{16} \, x^{6} - \frac {80595}{16} \, x^{5} - \frac {629505}{32} \, x^{4} - \frac {1661133}{32} \, x^{3} - \frac {28504029}{256} \, x^{2} - \frac {64029233}{256} \, x + \frac {290521 \, {\left (1080 \, x - 463\right )}}{1024 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {60160485}{256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 51, normalized size = 0.70 \[ \frac {\frac {39220335\,x}{512}-\frac {134511223}{4096}}{x^2-x+\frac {1}{4}}-\frac {60160485\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {64029233\,x}{256}-\frac {28504029\,x^2}{256}-\frac {1661133\,x^3}{32}-\frac {629505\,x^4}{32}-\frac {80595\,x^5}{16}-\frac {10125\,x^6}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 65, normalized size = 0.89 \[ - \frac {10125 x^{6}}{16} - \frac {80595 x^{5}}{16} - \frac {629505 x^{4}}{32} - \frac {1661133 x^{3}}{32} - \frac {28504029 x^{2}}{256} - \frac {64029233 x}{256} - \frac {134511223 - 313762680 x}{4096 x^{2} - 4096 x + 1024} - \frac {60160485 \log {\left (2 x - 1 \right )}}{256} \]
Verification of antiderivative is not currently implemented for this CAS.
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